The party planning committee has to determine the number of tables needed for an upcoming event. If a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people

Jude received the most votes among Luis, Joy, Jude, and Sally, with 31 percent of the votes according to the circle graph.

Based on the information provided in the circle graph, we can determine that:

Jude received 31% of the votes.

Sally received 25% of the votes.

Luis received 26% of the votes.

Joy received 18% of the votes.

To determine who received the most votes, we compare the percentages.

Among the four candidates, Jude received the highest percentage of votes, with 31%. Therefore, Jude received the most votes among Luis, Joy, Jude, and Sally.

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Answer:

GCF: 4

LCM: 60

The value of 2x - yz with x = 34, y = 0.2, and z = 6 we get 69.2.

Here it is given that

x = 34

y = -0.2

z = 6

We need to calculate 2x - yz

If we first calculate 2x then we get

2x = 2 X 34

= 68

Now, if we calculate -yz next then we see

yz = -0.2 X 6

= -1.2

Hence

- yz = -(-1.2)

= 1.2

Therefore, adding up these two we get

2x - yz

= 68 + 1.2

= 69.2

Hence the value of 2x - yz is 69.2

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Correct Question

Evaluate the expression 2x - yz , where x = 34 , y = -0.2, and z = 6

Answer:

x = 3

Step-by-step explanation:

the central angle of 118° is equal to the measure of the arc that subtends it , then

38x + 4 = 118 ( subtract 4 from both sides )

38x = 114 ( divide both sides by 38 )

x = 3

Answer:

\({ \underline{ \sf{it \: is \: - 6 \frac{33}{40} }}}\)

Step-by-step explanation:

\(2 \frac{5}{8} \times ( - 2 \frac{3}{5} ) \\ \\ = \frac{21}{8} \times - \frac{13}{5} \\ \\ = - \frac{273}{40} \\ \\ = - 6 \frac{33}{40} \)

Answer:

1/67

Step-by-step explanation:

Complete question

If X+2/3x is equal to 45. find the value of x​

Given the equation

x+2/3x = 45

Cross multiply

x+2 = 3x(45)

x+2 = 135x

x - 135x = -2

-134x = -2

x = 2/134

x = 1/67

Hence the value of x is 1/67

Answer:

Rotation

Step-by-step explanation:

Answer:

Answer is 18

Step-by-step explanation:

Substitute the variable.

2 x 9 =

Then solve

2 x 9 = 18

The relative frequency of class D is 0.35.

The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments.

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.

Consider the given partial relative frequency distribution.

  Class            Relative frequency

    A                         0.22

    B                         0.18

    C                         0.43

    D                            

Then,

We need to find the relative frequency of class D

We know that,

Sum of relative frequency is equal to one.

that is.

\($0.22+0.18+0.25+$\) relative frequency of class D=1

0.65 + relative frequency of class \($\mathrm{D}=1$\)

relative frequency of class D=1-0.65

=0.35

We get,

Relative frequency of class D Is 0.35

Therefore, the relative frequency of class D is 0.35

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Answer:

x=7+√15

x=7-√15

Step-by-step explanation:

Answer:  Richard is 22 and Teo is 9

Step-by-step explanation:

Answer:

The surface area of a solid object like a paperweight is calculated by adding the areas of all its faces. In this case, the paperweight is like a hexagonal pyramid, with a hexagonal base and six triangular sides. The base area has already been given as 93.6 square centimeters.

The six triangles are isosceles triangles, since the base of each triangle is a side of the hexagon, and the slant height is the same for each triangle.

The area of an isosceles triangle is given by the formula:

Area = 1/2 * base * height

For these triangles, the base is 6 cm (side length of the hexagon), and the height is the slant height, which is 12 cm.

So the area of one triangle is:

Area = 1/2 * 6 cm * 12 cm = 36 square cm

Since there are six such triangles, the total area of the triangular faces is:

6 * 36 square cm = 216 square cm

So, the total surface area of the paperweight is the area of the base plus the area of the six triangular faces, or:

93.6 square cm (base) + 216 square cm (sides) = 309.6 square cm

So the surface area of the paperweight is 309.6 square cm.

The mean absolute value of the numbers 85, 90, 68, 75, and 79 is 79.4.

To find the mean absolute value of a set of numbers, we need to sum up the absolute values of all the numbers in the set and then divide the sum by the total number of values.

Let's calculate the mean absolute value for the numbers you provided: 85, 90, 68, 75, and 79.

Find the absolute values of the numbers.

|85| = 85

|90| = 90

|68| = 68

|75| = 75

|79| = 79

Calculate the sum of the absolute values.

85 + 90 + 68 + 75 + 79 = 397

Divide the sum by the total number of values (5 in this case).

397 / 5 = 79.4

Therefore, the mean absolute value of the numbers 85, 90, 68, 75, and 79 is 79.4.

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So, three other polar coordinates with the same Cartesian coordinates as (7, 5π/6) are (7, 17π/6), (7, -7π/6), and (7, 29π/6).

To find three other polar coordinates with the same Cartesian coordinates as (7, 5π/6), we can use the fact that polar coordinates have periodicity. Adding or subtracting multiples of 2π to the angle will give us equivalent points.

(7, 5π/6) - Given point.

(7, 5π/6 + 2π) - Adding 2π to the angle gives us an equivalent point.

=> (7, 17π/6)

(7, 5π/6 - 2π) - Subtracting 2π from the angle gives us another equivalent point.

=> (7, -7π/6)

(7, 5π/6 + 4π) - Adding 4π to the angle gives us another equivalent point.

=> (7, 29π/6)

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The equation Q = -L³ + 15 represents the production function of Plainfield Electronics, where Q is the quantity of industrial control panels produced and L is the level of labor input.

In this production function, the term -L³ indicates that there is diminishing returns to labor. As the level of labor input increases, the additional output produced decreases at an increasing rate. The term 15 represents the level of output that would be produced with zero labor input, indicating that there is some fixed component of output. To maximize production, the firm would need to determine the optimal level of labor input that maximizes the quantity of industrial control panels produced. This can be done by taking the derivative of the production function with respect to labor (dQ/dL) and setting it equal to zero to find the critical points. dQ/dL = -3L². Setting -3L² = 0, we find that L = 0.

Therefore, the critical point occurs at L = 0, which means that the firm would need to employ no labor to maximize production according to this production function. However, this result seems unlikely and may not be practically feasible. It's important to note that this analysis is based solely on the provided production function equation and assumes that there are no other factors or constraints affecting the production process. In practice, other factors such as capital, technology, and input availability would also play a significant role in determining the optimal level of production.

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The fireworks will explode after 1.125 seconds of launching Firework B.

Distance = Speed × time

Let time = t

Firework A:

\(D(t) = 360t - - - (1)\)

Firework B:

\(D(t) = 280(0.25) + 280t\)

\(D(t) = 70 + 280t - - - (2)\)

Equate 1 and 2 :

\(360t = 280t + 70\)

Collection of like terms

\(360t - 280t = 70\)

\(80t = 70\)

\(t = 70/80\)

\(t = 0.875 seconds\)

\(0.875 + 0.25 = 1.125 seconds\)

Therefore, the fireworks will explode after 1.125 seconds of launching Firework B.

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Answer:

-∞ < x < 4

Step-by-step explanation:

→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x  ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.

No, he should not be surprised. New Jersey Transit claims that the 8:00 a.m. train arrives late in New York on an average of 15 days a month. This means that the probability of the train arriving late on 3 or more days in a month is relatively high.  

To estimate this probability, one can carry out a simulation. First, generate a list of 20 random numbers between 0 and 1. Each number represents a day in the month and the probability of the train arriving late. Next, assign each number a value of 1 if it is less than or equal to 0.15 (the probability of the train arriving late on any given day), and 0 if it is greater than 0.15. This represents the arrival status of the train on each day.

Finally, sum the list of numbers to obtain the total number of days the train arrived late. Repeat this process multiple times and calculate the probability of the train arriving late on 3 or more of the 20 days.

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To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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The time required for the ball to reach the ground is approximately 0.56 seconds, and the horizontal displacement covered by the ball is approximately 1.34 meters.

To find the time required for the ball to reach the ground, we can use the formula for vertical motion. Since the ball is thrown horizontally, the initial vertical velocity is 0 m/s. The height of the table is 1.6 m, so we can use the formula h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. Plugging in the values, we get 1.6 = (1/2)(9.8)t^2. Solving for t, we find t ≈ 0.56 seconds.

To find the horizontal displacement covered by the ball, we can use the formula d = vt, where d is the displacement, v is the initial horizontal velocity, and t is the time. Plugging in the values, we get d = 2.4 m/s * 0.56 s ≈ 1.34 meters.

Therefore, the time required for the ball to reach the ground is approximately 0.56 seconds and the horizontal displacement covered by the ball is approximately 1.34 meters.

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One equation you can use is y = -12x+752 and you plug in x = 8 to find y.

=================================================

Explanation:

x = number of minutes

y = depth of the submarine

Being at sea level means the depth is y = 0. Diving 752 ft below sea level means the depth is y = 752. It's tempting to make this negative since we're below sea level, but depth values are always positive. They are simply distances you are from the surface of the water. Negative distances are never possible. So this concept might be a bit tricky to get used to.

Possibly equally confusing is the fact that the "12 ft per minute" means the slope is -12. This is because the depth is getting smaller as the submarine gets closer to the surface (aka the sub is rising).

The equation is y = -12x+752. The equation is in the form y = mx+b with m = -12 as the slope and b = 752 as the y intercept. Note how the y intercept is the starting depth value.

From here, we plug in x = 8 to find where the sub is

y = -12x+752

y = -12*8+752

y = -96+752

y = 656

The submarine's depth after eight minutes is 656 feet

----------------------

An alternative equation to use is

y = 12x-752

which is very similar to the other one used earlier. All I did was flip the sign of each term. Now y represents the height of the sub. Negative y values indicate we're below the surface of the water. The slope being positive means the submarine is going upward. The negative y intercept indicates we're starting 752 feet below sea level. Plugging in x = 8 will lead to y = -656, which you'll need to make positive (since all depth values are positive).

As you can probably guess, the change from y = -12x+752 and y = 12x-752 is simply multiplying the right hand side by -1, which explains why the signs flip (and explains how the y value sign flips as well)

Area A of squares S₁, S₂, S₃ and S₄ are 1 square units, 4 square units, 9 square units and 16 square units. Perimeter P of squares S₁, S₂, S₃ and S₄ are 4 units, 8 units, 12 units and 16 units.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Let four squares are S₁, S₂, S₃ and S₄.

And the sides of squares S₁, S₂, S₃ and S₄ are 1 unit, 2 unit, 3 unit and 4 unit respectively.

To find the perimeter P and area A:

Area of the square = side x side

And the perimeter of the square = 4(side)

For square S₁,

Area of the square = 1x 1

Area of the square A = 1 square unit.

And the perimeter of the square P = 4(1) = 4 units.

For square S₂,

Area of the square = 2 x 2

Area of the square A = 4 square unit.

And the perimeter of the square P = 4(2) = 8 units.

For square S₃,

Area of the square = 3 x 3

Area of the square A = 9 square unit.

And the perimeter of the square P= 4(3) = 12 units.

For square S₄,

Area of the square = 4 x 4

Area of the square A = 16 square unit.

And the perimeter of the square P = 4(4) = 16 units.

Therefore, A of squares S₁, S₂, S₃ and S₄ are 1 square units, 4 square units, 9 square units and 16 square units. P of squares S₁, S₂, S₃ and S₄ are 4 units, 8 units, 12 units and 16 units.

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Answer:

5\(\sqrt{3}\)

Step-by-step explanation:

in a 30-60-90 triangle the ratio of sides, respectively, is 1 : \(\sqrt{3}\) : 2

you can set up a proportion like this to solve for 'x':

\(\sqrt{3}\) / 1 = 15 / x

cross-multiply:

\(\sqrt{3}\)x = 15

x = 15/\(\sqrt{3}\)

rationalize the denominator by multiply top and bottom by \(\sqrt{3}\)

you get 15\(\sqrt{3}\) ÷ 3 which is 5\(\sqrt{3}\)

The missing angles and arcs are matched as follows:

An angle is a geometric figure formed by two rays that share a common endpoint, known as the vertex. It is typically measured in degrees or radians and is used to describe the amount of rotation between two intersecting lines.


An arc of a circle is defined as a section of the circumference of the circle between two radii. This means that the arc is defined by two endpoints on the circumference of the circle that are connected by the arc.

Here is how the angles and arc were derived:

1) The sum of internal angles in Polygon COBA (kite) is 360°
∠CAB = 180° - 114° = 66° (Angles on a Straight line)

Since Line CO and BO are Radii of the same angle bisecting tangents DA and FA (perpendicularly) respectively, we can state that:

∠ACO = ∠ABO = 90°

Thus:

∠COB = 360° - 90°-90°-66°

∠COB =  114°


2) ∠DFA = 58°

We arrived at that by stating that:

∠DFA = 180° - ∠DAF - ∠ADF (Sum of angles in ΔADF)
∠ADF = 180° - 124° = 56°
Since we already know ∠CAB to be 66°, thus
∠DFA = 180° - ∠DAF - ∠ADF
∠DFA = 180° - 66- 56
∠DFA =  58°


3) ∠OCA is already proven to be = 90° on the basis of a line tangent to a circle postulate.

4) ∠EOB = 360° - ∠COB - ∠COE
We already know ∠COB to be = 114°

To get ∠EOB, we must derive ∠COE.
Recall that line tangent to a circle postulate.
This means

∠DCO = ∠DEC = 90°
Thus,

Since DCOE is a quadrilateral, and we have

∠CED = 56° (sum of angles on a straight line);

∠DEC = 90°; and

∠DCO = 90°

Thus, ∠COE = 360° - 90° - 90° - 56°

∠COE = 124°

Since
∠COE = 124° and

∠EOB = 360° - ∠COB - ∠COE,

Thus,

∠EOB = 360° - 114° - 124°,

∠EOB = 122°


5) Since ∡ CE = ∠COE (Definition of an Arc and an Angle)

Thus, ∡ CE = 124°

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The roles and relationships that exist amongst the producers, consumers, and decomposers in an ecosystem is described by the food chain.

The meaning of ecosystem is the complex of a community of organisms and its environment functioning as an ecological unit.

Producer is an organism that produces its own food e.g. photosynthesis in plants. Also known as the base of the food-chain.

Consumer is an organism that consumes (eats) either a producer or another consumer e.g. animals will solely eat plants (herbivore), solely animals (carnivore), or a combination of both (omnivore).

Studies are showing that most animals are omnivores. Even pre-concluded herbivores or carnivores are found to eat a small variety of both plants and animals in a pinch. E.g. a deer would eat a baby bird if it found it on the ground.

Decomposers are organisms that 'eat' and break up dying/decaying material e.g. earthworms and fungi.

All of this together is the food cycle.

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Answer:

$355

Step-by-step explanation:

if each pear is 60c and apples are 5c less...

60×5=300

300+55=355

because 60-5=55